In the previous article calculating the cost of elements in a piping system (*Pumps & Systems*, July 2014), the energy consumed and power cost balanced exactly to demonstrate the process. Seldom is life that exact. In the real-world plant, instruments are subject to inaccuracy, pumps may be worn, estimates may be off
or the full system may not be
accurately represented in the design documents.

This month’s article demonstrates how cross-validating the calculated results can ensure the energy cost balance sheet accurately reflects system operation.

The key to validating the results is to use multiple means for arriving at the operating cost of each item in the energy cost balance sheet. If the energy cost balance sheet does not add up, troubleshooting skills need to be employed to discover the reason for the difference.

This article will continue to use the example piping system presented in previous articles (see Figure 1).

## Prioritizing the System

The pump elements provide all the energy that enters the system. That energy is then consumed by the system’s process and control elements.

If the energy cost balance sheet does not balance, operators should begin looking for the source of the problem. The major energy users in the system should be examined, and operators should find methods to cross-validate the initial estimates.

## Pump Performance

In the example, the pump’s flow rate was determined using the manufacturer’s pump curve. With a known flow rate, the pump efficiency can be determined from the curve.

Because the pump efficiency is used in all energy cost calculations, ensuring the accuracy of the value is critical.

Inaccuracies can occur in real-life operating conditions. For example, if the pump has a worn impeller and excessive internal leakage, it no longer reflects the pump curve’s operation.

Figure 2 shows a pump curve for the process pump along with an example of the effect that excessive internal leakage can have on the pump curve.

Using the calculated head difference of 235 feet (ft), the worn impeller gives a flow rate of less than the 4,000 gallons per minute (gpm) used in the previous energy system balance.

In addition, the efficiency of a worn impeller would differ from the manufacturer-supplied test curve.

This would result in inaccurate power consumption and operation costs calculations.

Operators have other options to determine the flow rate through the pump, including portable ultrasonic flow meters.

These meters provide a reasonably accurate flow measurement in a pipeline without physically changing the piping system.

If the observed flow rate on the temporary flow meter equals the value determined using the pump head and the pump curve, the flow rate is validated, and the efficiency is validated by association.

If a power meter is installed on the motor driving the pump, the measured kilowatt (kW) value can be compared to the calculated power consumed using the pumps flow, head and efficiency values as show in Equation 1, at the bottom of page.

If the power into the motor as read on its power meter is the same as the calculated power consumption using Equation 1, the pump’s flow, head and efficiency values are validated.

Where:

Q = flow rate in gpm

H = pump head in ft

ρ = fluid density lb/ft^{3}

η_{P} = pump efficiency

η_{M} = motor efficiency

If a power reading is not available for the motor, the motor’s power consumption can be calculated by measuring the current and voltage supplied to the pump’s motor, then using Equation 2. The motor’s power factor can be read on its nameplate.

Where:

P_{3ϕMotor} = motor power in kW

V = voltage volts

I = current amps

Pf = motor power factor

If the calculated value of motor power equals the pump’s power consumption, the pump flow, head and efficiency values are validated.

## Tank Levels and Pressures

The tanks and vessels make excellent piping system boundaries. The energy at each tank can be determined by using the elevation of the liquid level in the tank and pressure on the liquid surface.

From these values the energy consumed for the static head component can be easily calculated.

The results can be cross-validated using installed pressure and level instrumentation.

The liquid level can be checked with a sight glass or by manually measuring the liquid level in the tank. The pressure in a closed vessel can be compared using the installed plant instrumentation, installed pressure gauges or a temporary pressure gauge.

## Control Valves

In last month’s example, the differential pressure across the control valve was calculated by subtracting the sum of the head losses of the process elements from the pump head. This approach is easy, but any errors made in the previous calculations will compound and can greatly reduce the energy cost balance sheet’s accuracy.

Valve manufacturers define the operation of control valves based on tests that are outlined in published industry standards. Manufacturers use the ANSI/ISA-75.01.01 Flow Equations for Sizing Control Valves to size control valves for piping systems. The data used in valve sizing can also be used to calculate the differential pressure across the control valve.

Equation 3 shows the basic formula for valve sizing.

Where:

C_{v} = manufacturer-supplied valve coefficient

Q = flow rate in gpm

F_{P} = piping geometry factor (unitless)

P_{1} = absolute pressure measured at valve inlet in lb/in2

P_{2} = absolute pressure measured at valve outlet in lb/in2

S = fluid specific gravity (unitless)

Rearranging the control valve sizing equation and solving for differential pressure results in Equation 4.

In the example system with a flow rate through the level control valve of 2,500 gpm, the control valve position is 65 percent. According to the manufacturer’s data for the control valve, the C_{v} at this position is 391.

The F_{P} of .9996 was calculated by the manufacturer and included in the valve data sheet. The specific gravity of the process fluid was calculated at .993. The flow rate through the level control valve was measured at 2,500 gpm. Inserting the values into Equation 4 provides the differential pressure across the control valve.

Converting the control valve’s differential pressure of 40.6 pounds per square inch (psi) to feet of fluid results in a head loss of 94.3 ft. This result for the control valve calculation validates the number from last month’s calculations.

## Process Equipment

The differential pressure across the process equipment was calculated using the pressure drop data supplied by the manufacturer and the flow rate obtained from the installed flow element. In the example, the heat exchanger pressure drop of 10 psi was assumed based on the manufacturer’s supplied data. If the heat exchanger tubes were fouled due to internal deposit, the actual differential pressure across the heat exchanger would be greater than the value used in the energy cost calculation.

The differential pressure across the process equipment can be validated by installing temporary pressure gauges.

Most process equipment has vent and drain lines installed for maintenance.

By installing temporary pressure gauges on the vent and drain lines—and correcting the pressure values for any difference in elevation of the gauges—the differential pressure and head loss across the item can be measured.

## Pipelines

In the example, the head loss in the individual pipelines was calculated, then used to determine the head loss in each circuit of the pipeline. This requires a large number of calculations.

The repetitive nature of the calculations makes this an excellent task to be performed using a computer. Online head loss calculators can be found by performing an Internet search. Commercially available computer programs can also greatly simplify the task.

Problems that could affect the head loss calculation include fouling or sedimentation in the pipelines, partially closed valves, or obstructions in the pipe, valves or fittings. Inaccurate determination of the pipe size or schedule, or inaccurate estimates of the number of fittings or pipe length can also affect the head loss calculation.

## Total System

If the energy cost balance sheet does not balance, either the measured plant data or the equipment (pumps, process components or control valves) could be causing the problem.

To confirm the accuracy of the measured data, check to see that the instruments are calibrated. The instrumentation department can also make sure the instruments are accurately reading the process parameters.

The first step is to check for cavitation throughout the whole system. Cavitation is caused when the local pressure drops below, then rises above, the vapor pressure of the process fluid. Some of the fluid is converted from liquid to vapor. The vapor bubbles take up extra space in the flow stream, which causes a reduction in the mass flow rate.

All standards and calculation methods used to determine head loss assume single phase flow. If cavitation occurs, the calculated results will not accurately reflect what is happening in the system.

Cavitation is especially troublesome in pumps and control valves. It can be a major source of maintenance problems and should be corrected prior to performing a system assessment.

Next, the interaction of the system’s components should be examined. The best way to accomplish this is to compare the current observed values with previous observed values.

For example, the average valve position of the level control valve increased over time from 65 percent open to 71 percent open. The rest of the measured plant data remained the same.

Using Equation 4, the head loss across the level control valve decreased from the original 94 ft of loss to 71 ft. The only explanation for this change is that the head loss across the process element increased from the manufacturer’s published value of 23 ft to 46 ft. This is a clear indication of fouling in the process equipment.

## Conclusion

Gaining a clear picture of how a piping system operates is key to assessing the system.

Because most operating plants do not have sufficient installed plant instrumentation to provide all the data needed for the calculations, many of the values must be calculated using other well-established methods.

By performing the calculations and comparing them to available operating data, operators can determine how the system is currently operating.

This information allows operators to correct any problems that adversely affect system operation and perform an accurate assessment of the piping system by completing an energy cost balance sheet.

My next few columns will investigate a variety of plant systems. They will demonstrate what can be gained with a better understanding of system operation and what can be done to reduce operating, maintenance and capital cost within piping systems.